有限群的SS-半置换p-子群与p-幂零性  

On SS-Semipermutable p-Subgroups and p-Nilpotency of Finite Groups

作　　者：李彬彬 钟祥贵 张博儒 卢家宽 Li Binbin;Zhong Xianggui;Zhang Boru;Lu Jiakuan(School of Mathematics and Statistics,Guangxi Normal University,Guilin Guangxi 541006,China)

机构地区：[1]广西师范大学数学与统计学院,广西桂林541006

出　　处：《西南师范大学学报（自然科学版）》2022年第10期54-58,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11861015,12161010);广西省自然科学基金项目(2020GXNSFAA 238045);广西省自然科学基金项目(2020 GXNSFBA297121);2020年度广西高校中青年教师科研基础能力提升项目(2020KY02019)

摘　　要：设G是有限群,H是群G的子群.如果群G中存在子群B使得G=HB,并且H与B的所有Sylow p-子群置换,其中素数p满足(p,|H|)=1,则称H在G中SS-半置换.假设P是群G的Sylow p-子群,D是P的非平凡子群.利用有限群G的Sylow p-子群P的|D|阶子群的SS-半置换性来研究有限群G的结构,给出了有限群G是p-幂零群的两个充分条件.Let G is a finite group,and H is a subgroup of G.If there exists a subgroup B of G such that G=HB and H permutes with all of Sylow p-subgroup of B,where prime p is a coprime with the order of H,then H is SS-semipermutable group of G.Suppose P is a Sylow p-subgroup of group G and D is a nontrivial subgroup of P.In this note,two sufficient conditions for a Sylow p-nilpotency of finite group G are obtained by using the SS-semipermutation of some subgroups of Sylow p-subgroup of group G.

关 键 词：P-子群 SS-半置换 P-幂零 

分 类 号：O152.1[理学—数学]